In the present research analysis we have addressed comparative investigation of radiative electrically conducting Casson nanofluid. Nanofluid Flow is assumed over a nonlinearly stretching sheet. Heat transport analysis is carried via joule dissipation, thermal behavior and convective boundary condition. To employ the radiative effect radiation was involved to show the diverse states of nanoparticles. Furthermore entropy optimization with activation energy and chemical reaction are considered. Thermodynamics 2 nd law is applied to explore entropy generation rate. Nonlinear expression is simplified through similarity variables. The reduced ordinary system is tackled through optimal approach. Flow pattern was reported for wide range of scrutinized parameters. Computational consequences of velocity drag force, heat flux and concentration gradient are analyzed numerically in tables. Results verify that conduction mode augments with enhance of magnetic parameter. Increasing radiation boosts the temperature and entropy. Activation energy corresponds to augmented concentration. Heat transmission rate augments with the consideration of radiation source term. The researcher has grown consideration in the non-Newtonian fluids due to their remarkable features in the area of technological and industrial sciences. For instance, synthetic lubricants, drilling muds, certain oils, paints, sugar solutions, clay coating, and biological fluid like blood are the just communal cases of non-Newtonian fluids. The Navier-Stokes fundamental equations cannot momentarily define the characteristics of the flow field of non-Newtonian fluids due to the complexity in the mathematical formulation of the flow problem. Abundant models for non-Newtonian fluids are defined as deliberate rheological qualities such as Eyring-Powell, Bulky, Seely, Oldroyd-B, Maxwell, Oldroyd-A, Carreau, Casson, Burger, Jeffrey, etc. Amongst these models, the most significant model for the blood properties and suspensions in our daily life is the Casson model 1. For the purpose of developments in fluids study, considering Soret and Dufour effects, Hayat et al. 2 proposed the flow of Casson fluid. The details research work about Casson fluid can be seen in 3-6. Saravana et al. 7 have been studied magnetohydrodynamic Casson fluid with inconstant thickness under the aligned magnetic field. Due to its frequent uses in engineering and industrial, the theme of nanofluidic flow has attracted widespread attention over the past two decades. Researchers and scientists have not only discovered the astonishing thermal properties of nanofluids, but improving the causes of thermal conductivity of nanofluids are also planned, the integration of biotechnological mechanisms and nanofluids may provide capable applications in biosensors, agriculture and pharmaceuticals. In the biotechnology field, there are many nanomaterials in practice, such as

A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets ( SFS ) . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries.

In this article, the magnetohydrodynamic flow and heat transmission of a micropolar hybrid nanofluid between two surfaces inside a rotating system are examined. The Hall current and thermal radiations are also considered for the flow system. In this article, a base fluid is taken as water, while graphene oxide (GO) and copper (Cu) are applied as hybrid nanoparticles. The flow is assumed to be in a steady state. The governing partial differential equations along with boundary conditions for the modeled problem are transformed into a system of non-linear ordinary differential equations using similarity transformations. The set of resultant ordinary differential equations is solved by using an optimal approach. The main focus of this study is to examine the magnetohydrodynamic heat transmission and hybrid nanofluid flow in a rotating system between two parallel plates by taking into account the thermal radiations and Hall current impacts. Various physical parameters are discussed in detail graphically in this article. The main outcome of this study indicates that the augmented values of the magnetic parameter increase the velocity profile and decrease the rotational velocity profile.

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In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction. A strong convergence result is provided under some mild conditions, and an iterative sequence is accomplished without previous knowledge of the Lipschitz-type constants of a cost bifunction. A sufficient explanation is that the method operates with a slow-moving stepsize sequence that converges to zero and non-summable. For numerical explanations, we analyze a well-known equilibrium model to support our well-established convergence result, and we can see that the proposed method seems to have a significant consistent improvement over the performance of the existing methods.

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This research work deals with investigation of the thermal characteristics of the Darcy–Forchheimer hydromagnetic hybrid nanofluid (Al2O3-Cu/H2O) flow through a permeable stretching cylinder. The model equations, which consist of continuity, momentum, and energy equations, are converted to a set of coupled ordinary differential equations through similarity variables transformations and appropriate boundary conditions. Brownian motion and Thermophoresis effects are mainly focused in this work. The impacts of some interesting parameters over velocity, temperature, and concentrations profiles are graphically studied. The present study will be helpful in understanding the thermal characteristics of heat transfer liquids.

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